OCR A-level Mathematics A · H240

Extreme

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Extreme practice · Multi-step problems within A-level pure maths. Difficulty is an editorial judgement. These questions are self-reviewed, not ranked.

OCR format & instructions

Calculator permitted. Give clear working in the answer booklet and label each part. Formulae are provided in the official question paper.

Original topic practice. This set is not a full official paper. Written work is self-reviewed against our worked solutions.

01 · Pure · 100 marks · 2 hours
02 · Pure & statistics · 100 marks · 2 hours
03 · Pure & mechanics · 100 marks · 2 hours

Official specification ↗ · Official past papers ↗

QUESTION PAPER

Mathematics · A levelPure mathematics · H240/01

Torus Maths original · OCR style

For $|x|<1/3$ , $f(x)=(1+3x)^{-1/2}+(1-3x)^{-1/2}-2$ .

(a)

Find the terms in x² and x⁴ in the expansion of f(x). State why the odd powers vanish.

[4]

(b)

For small positive ε, the small positive solution of $f(x)=3\varepsilon^2/4$ is approximated by $x=(\varepsilon+c\varepsilon^3)/3$ . Find c by retaining terms through ε⁴.

[4]

Question reference: ocr-a-level-extreme-09-01Report a question →

Answer booklet

Question 1 · Show your working

(a)

Answer booklet · Question 1(a)

(b)

Answer booklet · Question 1(b)

Need a nudge?Three small hints · no answer revealed